Chop the garlic finely. Sprinkle 1 tablespoon salt over the garlic and continue to chop it, occasionally smashing and smearing the garlic with the flat side of the knife, until the garlic becomes pastelike. (Alternatively, mash the garlic and salt together in a mortar and pestle.) Put the garlic paste, butter, thyme, and pepper in a small bowl. Fold the softened butter over and onto the garlic and thyme, mashing it down with the back of a spoon or spatula. Use a sheet of plastic wrap to help shape the butter into a log, wrap the log well with the plastic wrap, and refrigerate until ready to use. (The garlic butter can be made up to 3 days ahead; it can also be frozen, well wrapped, for a couple of months.)
Melt half of the garlic-butter mixture in a small pan over medium heat. (Rewrap and save the other half for future use; it's great stuff under the skin of a chicken before roasting or tossing into the broth of steamed mussels.)
Heat the oven to 425 degrees F.
In a large ovenproof saute pan, heat the vegetable oil over high heat until very hot. Season the steaks with a little salt and pepper. Add the steaks to the pan and brown them well on 1 side, about 5 minutes. Turn the steaks and brush them liberally with the garlic butter. Finish cooking the steaks in the oven, brushing them occasionally with more garlic butter, until done, about another 5 minutes. (The time will vary depending on how you like your steaks cooked and how thick they are.) Remove the steaks from the oven and allow them to rest for 5 minutes before serving. Serve smaller steaks whole or sliced thinly across the grain. Cut larger steaks into 2 servings or into thin slices. Spoon any remaining juices from the pan onto the meat as well.